Water Flow in Glaciers

1. Water Flow in Glaciers 1. Introduction 2. Water sources 3. Water flow (a) permeability (b) hydraulic potential (c) pressure and conduit size (d) direction of flow (e) unsteady state conditions 4. Storage 5. Subglacial drainage systems (a) Discrete systems (b) Distributed systems

2. References Bennett, M.R. and Glasser, N.F. (1996) Glacial geology: ice sheets and landforms. Wiley, Chichester. Chapter 4 Glacial meltwater

3. Introduction What is the impact of water in glaciers? • In mass balance • Sliding • Subglacial sediment deformation • Hydrological systems • Sediment transport

4. Water sources Sources • ice melt • snow melt • rainfall • runoff from ice-free slopes • release of stored water

5. Surface melting • temperature • radiation flux • highly variable in time and space Rainfall • rain on snow events • greater runoff generation • highly variable in time and space Englacial and subglacial melt • friction from ice deformation (sliding) • more constant in time?

7. Water flow Permeability • primary permeability • secondary permeability

8. Primary permeability • intact ice and snow • high for snow and firn - linked pore spaces • very low for ice • ice at pmp interconnected veins and lenses between ice crystals Secondary permeability • tunnels and passage ways (mm - m's) • most water draining through glaciers

9. Hydraulic potential Available energy at a particular time and place • Surface streams - potential depends on elevation • At base - depends on elevation and pressure In an englacial or subglacial stream: f = f0 + fe + Pw • where • Ø = hydraulic potential • Ø0 = a constant (conduit size & shape) • Øe = elevation potential • Pw = water pressure

10. The elevation potential is the product of the weight of water and it elevation: fe = rw.g.z where w = water density g = gravitational acceleration z = elevation

11. In natural conditions water pressure can vary between: • atmospheric • cryostatic Cryostatic pressure is the product of the weight and thickness of the ice: Pi = ri.g.(H-z) where Pi = ice pressure i = ice density H = altitude of the ice surface z = elevation at site

12. Vadose zone • connected with the atmosphere • at atmospheric pressure • potential depends on elevation Phreatic zone • saturated • no air in conduits • above atmospheric pressure

13. Effective pressure N = Pi - Pw When Pw is zero the effective pressure is the cryostatic pressure Controls • glacier motion • bed deformation

14. If Pw = Pi (ie N=0) • the water can support the whole weight of the glacier • the water can lift the glacier off its bed Local scale • where cryostatic pressures are lower than normal • eg downstream side of protuberances Large scale • subglacial lakes

15. Pressure and conduit size Pressure in water filled conduits controlled by: Frictional heat • melt and passage enlargement Ice deformation • pressure gradient between the ice and water • tendency to decrease passage size

16. Equilibrium conditions Pw = Pi + Pm where Pm = pressure change to melting or contraction

17. Negative Pm • pressure drop due to efficient melting • melt rates increase with increasing passage radius • Larger channels • carry more water • dissipate more heat to the area of their walls Positive N (N = Pi – Pw ) • ice deformation rates increase • large pressure differences between the water conduit and ice lead to rapid closure

18. Two important implications: 1. Melting and deformation allow conduit expansion and contraction in response to Pw increases and decreases If Pw increases N falls, reducing conduit closure rates • Þ passages can only become larger through melting If Pw falls, the increased pressure gradient between the ice and water accelerates closure until an equilibrium is reached Þ Enlargement by by melting is rapid (hrs) Þ Contraction change by ice deformation is slow days - weeks)

19. 2. Because melt rates increase with conduit radius Inverse relationship between water pressure and conduit radius Largest passages have lowest pressures • Þ water will flow toward larger channels following the pressure gradient • Þ large passages grow at expense of smaller ones • Þ branching networks

20. Direction of flow Direction of flow determined by hydraulic potential Equipotential lines: • the pressure of the overlying ice is equal to water pressure it generates • Geometry determined by • variation in ice thickness (major) • slope of underlying topography (minor) Once it reaches the bed water will flow to the snout at right angles to equipotential contours • defined by intersections of equipotential surfaces with the bed

23. Non steady state conditions Equation for water pressure (Pw=Pi+Pm) is based on a steady state condition • internal plumbing in equilibrium • considered reasonable under normal conditions • ok for basal melting Rapid fluctuations • high discharges rapidly fed from surface • water backs up faster than conduits can enlarge • opposite to inverse relationship between conduit radius and Pw

24. However: • conduits enlarge rapidly and close slowly • therefore the most common condition is a low pressure system • water pressure close to atmospheric during most of ablation season • tendency for vertical englacial drainage • tendency for subglacial drainage to follow the slope

25. Storage Water storage in lakes and ponds if a barrier exists • subglacial • englacial • supraglacial • proglacial

26. Subglacial Scale mm-2 to 1000's km-2 eg 8000 km-2 beneath the east Antarctic ice sheet Areas of low hydraulic potential surrounded by high hydraulic potential

28. Supraglacial and englacial Usually temporary Englacial - usually closed conduits or crevasses Seasonal supraglacial lakes on temperate glaciers

31. Ice dammed lakes Glacier ice forming a barrier to local or regional drainage Settings: • ice-free valley sides blocked by a glacier • in trunk valleys where a glacier has blocked drainage • a junction between two valley glaciers Polar and subpolar glaciers eg Glacial Lake Agassiz Hudson Bay-draining rivers

32. Proglacial lakes Topographic barriers moraines over-deepened troughs

33. Subglacial drainage systems Importance • ice velocity • glacier stability • bed deformation • sediment erosion, transport and deposition Discrete and distributed systems • efficiency

34. Discrete systems Rothlisberger channels (R-channels) Nye channels (N-channels) Tunnel Valleys Distributed systems Films Linked cavity networks Braided canal networks Porewater flow

35. R-channels Incised upwards into the ice • floored by rock Steady state pressures lower than cryostatic pressure Path governed by hydraulic gradient at the bed • surface slope (large impact) • bed gradient (small impact) May flow uphill In valley glaciers tendency to flow away from the centre line • driven by convex profiles

36. Evidence • tunnel portals • boreholes • Eskers • Dye tracing

37. N-channels Incised into the substrate Single channels and braided networks Imply erosion in a concentrated areas • topographic focusing? Evidence • Former channels in bedrock • Modern observations • Dye tracing

38. Tunnel Valleys Branching channel networks in soft sediment • Bottom - N-channel • Top -R-channel Develop to allow efficient drainage of subglacial aquifers (Boulton and Hindmarsh 1987) Evidence • Glacial geologic record

39. Water films Thin films carrying most discharge (Weertman 1972) More than 1mm, tend to channel (theory - Walder 1982) Therefore limited ability to carry water Source • local pressure melting? • protuberances • regelation Particle sizes used to reconstruct film thickness (eg Calcite beds - Hallet) Most cases thinner than a few m

40. Linked cavity systems Cavities develop between the base of the ice and bedrock Lliboutry (1986, 1979) Linked by narrow orifices Low velocities and transit times Evidence • Reconstructions from limestone terrains • cavities identifiable from solution features • Dye tracing • diffuse, multi-peaked returns

41. Opposite behaviour to R-channels • channels: negative relationship between discharge and pressure • cavities form where Pw>Pi • therefore increases in water pressure result in increases in capacity (Q) • no tendency to capture melt from smaller cavities • tend to be stable features Breaks down a high discharges where melting becomes important pressure in cavity maintenance • mode switch for surging? (Kamb 1987)

45. Braided canal systems Branching, low pressure channels develop in till when Darcian flow cannot evacuate the water (Shoemaker 1986) Modeling: (Walder and Fowler 1994) • predicts dendritic drainage system unstable unless the • substrate is very stiff • speculation on wide, braided systems of canals • pressure relations similar to linked cavity system • a stable, distributed system Argument that should be recognisable in the geologic record • broad lenses of sorted sediments

46. Porewater Movement Rock beds - insignificant (ex. Limestone) Unconsolidated sediments Two mechanisms 1. Bulk movement • water carried with mineral grains 2. Darcian flow • flow relative to mineral grains • driven by a hydraulic gradient

47. Where k = hydraulic conductivity A = sample cross-sectional area transverse to flow n = fluid viscosity Dp/d = pore water pressure gradient

48. The hydraulic conductivity of most sediment is low • discharges will be low unless pressures are very high • not efficient, unlikely to evacuate the large amounts of water • probably occurs alongside other mechanisms Connections between porewater and channel flow established (Hubbard et al. 1995, Boulton & Hindmarsh, 1987) • High pressure - water forced into till • Low pressure - water returned to channel

50. Bed depressions • steeper than equipotenial lines • ponding occurs because hydraulic potential increases towards the edges of the depression